⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢠⣠⣤⠤⠶⠶⠒⠚⠛⠋⠉⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣀⣴⠶⠒⠒⠛⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠦⣤⣤⣀⣀⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠈⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⠛⢷⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠚⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡿⠀⠈⢿⣄⣰⡾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠓⢲⡖⠒⠒⠒⠒⠒⠒⠛⠀⠀⣀⣀⢀⣀⣀⣀⣤⣿⣇⠛⠁⠀⠀⠀⠉⠉⠀⣠⣴⣾⠛⠛⠛⠿⣿⣶⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠛⠋⠉⠉⠉⠈⢻⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⢷⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠋⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⡤⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠁⠀⢀⣤⢤⣤⡀⠀⠀⠈⡇⠀⠀⢠⡟⠀⠀⠀⢠⣶⠖⠶⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⣤⠬⠿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⡏⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⢿⣤⣤⡶⠋⠀⠀⠀⠈⠛⠳⠶⢺⡏⠀⠀⠀⠀⠀⠙⠛⣶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⣇⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠛⠋⢀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠀⡄⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⠀⠀
⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡀⠈⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠠⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⠀⠀
⠀⠀⠀⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣈⣁⣀⣀⣶⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⢉⣿⠃⠀⠉⢉⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀
⠀⣼⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠸⠏⠀⠀⠀⠸⠇⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠃⠀
⠀⠀⠀⢸⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣶⣤⣤⣤⣤⣴⡶⠞⢉⣡⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠓⠲⠶⠤⠤⠤⠴⠶⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⣤⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀